1. **State the problem:** Simplify the expression $$\frac{5(2x - 3) + 6(3y + 4)}{30}$$. 2. **Apply the distributive property:** Multiply inside the parentheses: $$5(2x - 3) = 10x - 15$$ $$6(3y + 4) = 18y + 24$$ 3. **Add the results:** $$10x - 15 + 18y + 24 = 10x + 18y + 9$$ 4. **Rewrite the expression:** $$\frac{10x + 18y + 9}{30}$$ 5. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (3):** $$\frac{\cancel{3}(\frac{10x}{3} + 6y + 3)}{\cancel{3} \times 10} = \frac{10x/3 + 6y + 3}{10}$$ 6. **Express the simplified form:** $$\frac{10x}{30} + \frac{18y}{30} + \frac{9}{30} = \frac{1}{3}x + \frac{3}{5}y + \frac{3}{10}$$ **Final answer:** $$\frac{1}{3}x + \frac{3}{5}y + \frac{3}{10}$$